I'm trying to understand Fourier series and in order to do so have to be able to calculate the partial derivates of the function:
I_n=(Integral [ f(x) - a_0/2 - sigma (a_k cos(kx) + b_k sin(kx)]^2)dx
w.r.t. a_0, a_k and b_k, where the integral is calculated from -pi to pi.
I actually had certain thoughts about how to go about this, which I originally wrote here, but as I quickly realized it was completely wrong I've deleted this... Now I'm thinking like this: it's a definite integral, so if I calculate the primitive functions of all the terms containing x, and then calculate the partial derivatives that should do it, no?
Still, I don't get the answer in my book... So....
If someone could explain to me how to go about this in an easy-to-understand, step-by-step manner it'd be greatly appreciated!